Harmonic Model Description of the Franck−Condon Density for a Betaine Dye Molecule

Zwitterions Functionalized by Optical Cycling Centers: Toward Laser-Coolable Polyatomic Molecular Cations

Functionalization of large aromatic compounds and biomolecules with optical cycling centers (OCC) is of considerable interest for the design and engineering of molecules with a highly selective optical photoresponse. Both internal and external dynamics in such molecules can be precisely controlled by lasers, enabling their efficient cooling and opening up broad prospects for high-precision spectroscopy, ultracold chemistry, enantiomer separation, and various other fields. The way the OCC is bonded to a molecular ligand is crucial to the optical properties of the OCC, first of all, for the degree of closure of the optical cycling loop. Here we introduce a novel type of functionalized molecular cation where a positively charged OCC is bonded to various organic zwitterions with a particularly high permanent dipole moment. We consider strontium(I) complexes with betaine and other zwitterionic ligands and show the possibility of creating efficient and highly closed population cycling for dipole-allowed optical transitions in such complexes.

Innovative mass spectrometer for high-resolution ion spectroscopy

Conventional ion spectroscopy is inapplicable for ions produced in low concentrations or with low spectral resolutions. Hence, we constructed a high-resolution vacuum ultraviolet mass-analyzed threshold ionization (HR VUV-MATI) spectrometer composed of a four-wave frequency mixing cell capable of generating long-lasting and intense VUV laser pulses of ∼1 × 10¹⁰ photons/pulse at wavelengths of 123.6-160.0 nm, a space-focused linear time-of-flight photoionization chamber with a new ion-source assembly, and a compact molecular beam chamber with a temperature-controlled pulsed nozzle for ion spectroscopy. The ion-source assembly and pulsing schemes enabled an ∼15-μs-delayed but extremely weak pulsed-field-ionization of the molecules in the zero-kinetic-energy (ZEKE) states and first-order space focusing of the generated MATI ions. These ZEKE states were effectively generated by a minute electric jitter from the high-lying Rydberg states, which were initially prepared via VUV photoexcitation. The spectral and mass resolutions (∼5 cm^-1 and 2400, respectively) and the signal strength were simultaneously enhanced using this spectrometer. Moreover, it could be used to measure the fine vibrational spectrum from the zero-point level of the cation and the exact adiabatic ionization energy of the neutral molecule. Additionally, it could be used to measure the appearance energies of the photoproducts and elucidate the vibrational structures of the cationic isotopomers, utilizing other pulsing schemes. Furthermore, this spectrometer could be used to analyze the congested vibrational spectrum of a cation with multiple conformations. Thus, the HR VUV-MATI spectrometer-a potential alternative to photoelectron spectrometers-can be used to analyze the conformational structure-dependent reactivities.

Conformational structure of cationic tetrahydropyran by one-photon vacuum ultraviolet mass-analyzed threshold ionization spectroscopy

Isolating and identifying the conformational forms of molecules are imperative processes to investigate the chemical reaction pathways of individual conformers. Herein, we explored the conformational structures of tetrahydropyran in the neutral (S0) and cationic (D0) states by varying the supersonic expansion conditions using one-photon vacuum ultraviolet mass-analyzed threshold ionization (VUV-MATI) spectroscopy. The constructed 2D potential energy surfaces associated with conformational interconversion between the chair and boat forms in the S0 and D0 states revealed that the ionic transitions observed in the MATI spectra correspond to the most stable chair conformer. Accordingly, based on the 0-0 band in the VUV-MATI spectrum supported by the VUV photoionization efficiency curve, the adiabatic ionization energy for the conversion of the chair conformer to a cationic state was determined to be 74 687 ± 4 cm-1 (9.2600 ± 0.0005 eV). Definitive vibrational assignment of the measured MATI spectra using Franck-Condon fitting revealed the cationic structure of the twisted chair conformer. The geometrical change upon ionization promoted the vibrational modes associated with ring inversion and deformation motions in the cationic state. This behavior, which was attributed to the effect of electron removal from the highest occupied molecular orbital (HOMO) consisting of the nonbonding orbital of the oxygen atom, reveals the role of electrons in the HOMO.

The absorption and fluorescence spectra of 4-(3-methoxybenzylidene)-2-methyl-oxazalone interpreted by Franck-Condon simulation in various pH solvent environments

The absorption and fluorescence spectra of 4-(3-methoxybenzylidene)-2-methyl-oxazalone (m-MeOBDI) dissolved in neutral, acidic, and basic solvent environments have been investigated and assigned by using Franck-Condon (FC) simulations at the quantum TDDFT level. Four different structures of m-MeOBDI in the ground and excited states are optimized and are found to be responsible for the observed absorption and fluorescence spectra. The (absorption) fluorescence of m-MeOBDI in pure methanol and neutral/basic methanol/water (1/9 vol) mixed solvent is found to arise from the (ground neutral N-I) excited neutral N-I* and cationic C-III* species, respectively. In acidic solvent, the absorption is found to arise from ground acidic C-II species, and the excited divalent cation DC-IV* is found to be formed in its excited state due to the excess H⁺ in the solution, and then it emits ∼560 nm fluorescence. FC simulations have also been employed to confirm our assignments as well as interpret the vibronic band profiles. As expected, the simulated emission spectrum of the divalent cationic species is in good agreement with the experimental observation. Therefore, within the present FC simulation, the observed absorption and fluorescence spectra have been reasonably interpreted and novel fluorescence mechanisms of m-MeOBDI in various pH solvent environments have been proposed.

Extremely solvent-enhanced absorbance and fluorescence of carbazole interpreted using a damped Franck-Condon simulation

Extremely solvent-enhanced absorption and fluorescence spectra of carbazole were investigated by performing a generalized multi-set damped Franck-Condon spectral simulation. Experimental absorption and fluorescence spectra of carbazole in the gas phase were first well reproduced by performing an un-damped Franck-Condon simulation, but a one-set scaling damped Franck-Condon simulation severely underestimated the intensities of the peaks of experimental absorption and fluorescence spectra of carbazole in n-hexane. Then, a multi-set scaling damped Franck-Condon simulation was proposed and carried out for simulating the extremely solvent-enhanced absorbance and fluorescence, and here, the simulated spectra agreed well with the experimental ones. Five (four) representative solvent-enhanced normal modes corresponding to the combination of ring stretching and ring breathing vibrational motions were determined to be responsible for enhanced absorbance (fluorescence) in n-hexane solution. Furthermore, different scalings were applied to the ground and first-excited states, resulting in different enhancement of absorbance and fluorescence, and this analysis revealed atoms in the carbazole interacting with n-hexane solvent molecules and, hence, leading to different normal-mode vibrational vector patterns in the ground and first-excited states, respectively. Basically, the same conclusion was drawn from a simulation with HF-CIS and the three functionals (TD)B3LYP, (TD)B3LYP-35, and (TD)BHandHLYP. The present multi-set scaling damped Franck-Condon simulation scheme was demonstrated to successfully interpret extremely solvent-enhanced absorbance and fluorescence of carbazole in n-hexane-solvent.

Digital quantum simulation of molecular vibrations

Molecular vibrations underpin important phenomena such as spectral properties, energy transfer, and molecular bonding. However, obtaining a detailed understanding of the vibrational structure of even small molecules is computationally expensive. While several algorithms exist for efficiently solving the electronic structure problem on a quantum computer, there has been comparatively little attention devoted to solving the vibrational structure problem with quantum hardware. In this work, we discuss the use of quantum algorithms for investigating both the static and dynamic vibrational properties of molecules. We introduce a physically motivated unitary vibrational coupled cluster ansatz, which also makes our method accessible to noisy, near-term quantum hardware. We numerically test our proposals for the water and sulfur dioxide molecules.

Franck–Condon simulation for unraveling vibronic origin in solvent enhanced absorption and fluorescence spectra of rubrene

The damped FC method shows how and which local modes are responsible to solvent enhance vibronic spectra.

Theoretical study of geometrical and nonlinear optical properties of pyridinum N-phenolate betaine dyes

This paper presents an ab initio quantum chemical investigation of the geometrical structures and the non-linear optical properties (NLO) of three structural isomers of pyridinium N-phenolate betaine dye. The ground state geometrical parameters and the first-order hyperpolarizabilities were calculated using the Hartree-Fock (HF) as well as the second-order perturbation Møller-Pleset (MP2) method with the 6-31G, 6-31G(d), 6-31G(d,p), 6-31+G(d), 6-31++G(d,p), 6-311+G(d), aug-cc-PVDZ and the recently developed Z3PolX basis sets. Moreover, the first-order hyperpolarizability was calculated at the coupled cluster singles and doubles (CCSD/6-31+G(d)) level of theory. The analysis of the results of calculations for the investigated isomers indicates that there are important differences in their NLO activities. Additionally, it was shown that Z3PolX basis set works reasonable well for betaine dyes.

Ultrafast electron-transfer and solvent adiabaticity effects in viologen charge-transfer complexes

We report ultrafast electron transfer (ET) in charge-transfer complexes that shows solvent relaxation effects consistent with adiabatic crossover models of nonadiabatic ET. The complexes of either dimethyl viologen (MV) or diheptyl viologen (HV) with 4,4'-biphenol (BP) (MVBP or HVBP complexes) have identical charge-transfer spectra and kinetics in ethylene glycol with approximately 900 fs ET decay. We assign this decay time as largely due to adiabatic control of a predicted approximately 40 fs nonadiabatic ET. The MVBP decay in methanol of 470 fs is reduced in mixtures having low (2-20%) concentrations of acetonitrile to as short as 330 fs; these effects are associated with faster relaxation time in methanol and its mixtures. In contrast, HVBP has much longer ET decay in methanol (730 fs) and mixture effects that only reduce its decay to 550 fs. We identify the heptyl substituent as creating major perturbations to solvent relaxation times in the methanol solvation shell of HVBP. These charge-transfer systems have reasonably well-defined geometry with weak electronic coupling where the electronic transitions are not dependent on intramolecular motions. We used a nonadiabatic ET model with several models for adiabatic crossover predictions to discuss the small variation of energy gap with solvent and the ET rates derived from adiabatic solvent control. A time correlation model of solvent relaxation was used to define the solvent relaxation times for this case of approximately zero-barrier ET.

Quantum Simulation of Solution Phase Intramolecular Electron Transfer Rates in Betaine-30

Mixed quantum-classical atomistic simulations have been carried out to investigate the mechanistic details of excited state intramolecular electron transfer in a betaine-30 molecule in acetonitrile. The key electronic degrees of freedom of the solute molecule are treated quantum mechanically using the semiempirical Pariser-Parr-Pople Hamiltonian, including the solvent influence on electronic structure. The intramolecular vibrational modes are also treated explicitly at a quantum level, with the remaining elements treated classically using empirical potentials. The electron-transfer rate, corresponding to S1 --> S0 relaxation, is evaluated via time-dependent perturbation theory with the explicit inclusion of the dynamics of solvation and intramolecular conformation. The calculations reveal that, while solvation dynamics is critical to the rate, the intramolecular torsional dynamics also plays an important role. The importance of the use of multiple high-frequency quantum modes is also discussed.

Franck−Condon Simulations of Clusters: Phenol−Nitrogen

Multidimensional Franck-Condon simulations of the resonance enhanced multiphoton ionization (REMPI) and mass-analyzed threshold ionization (MATI) spectra of phenol-nitrogen are obtained from CASSCF, MRCI, and SACCI optimized geometries. In the REMPI simulations, the results are unsatisfactory, as the transitions associated with intermolecular modes are widely underestimated and much less intense than those associated with intramolecular modes. Conversely, the simulations of the MATI spectra show a good similarity to experiment. The best simulations are obtained in both instances from the SACCI optimized geometries. Furthermore, the simulations suggest that the two most prominent Franck-Condon envelopes present in the MATI spectra are due to the sigma and sigma + ngamma' combination bands in accord with the assignments of the MATI spectra of the analogous phenol-carbon monoxide cluster.

The Use of Multidimensional Franck−Condon Simulations to Assess Model Chemistries: A Case Study on Phenol

Multidimensional Franck-Condon simulations of the dispersed fluorescence spectra of phenol generated with geometries obtained from the highly correlated post-Hartree-Fock methods CASSCF, MRCI, and SACCI are presented. While the simulations based on CASSCF and MRCI optimized geometries are very similar to each other and fail to reproduce the experimentally measured intensities faithfully, the simulations obtained from SACCI optimized geometries are very close to the experimental spectra. The code developed for the multidimensional Franck-Condon simulations is described. It is shown that the integral storage problem common to the evaluation of multidimensional Franck-Condon integrals can be overcome by saving all quantities needed to disk. This strategy allows the code to run on computers with limited resources and is very well suited for application to molecules with a very large number of vibrational modes.